`(sqrt(5)-2sqrt(3))(sqrt(2)-2sqrt(2))`

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

Show that : (3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(2sqrt(3))/(sqrt(3)-sqrt(2))=11

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

Simplify: (2sqrt(2)+sqrt(3))/(2sqrt(2)-sqrt(3))

(sqrt(6+2sqrt(5)))(sqrt(6-2sqrt(5)))

(1)/(2sqrt(5)-sqrt(3))-(2sqrt(5)+sqrt(3))/(2sqrt(5)+sqrt(3)) =

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

Rationalize the denominatiors of : (2sqrt(5)+3sqrt(2))/(2sqrt(5)-3sqrt(2))

Simplify each of the following expressions: (i) (3+sqrt(3))(2+sqrt(2)) (ii) (3+sqrt(3))(3-sqrt(3)) (iii) (sqrt(5)+sqrt(2))^2 (iv) (sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))

Simplify the following expressions: (i) (3+sqrt(3))\ (3-sqrt(3)) (ii) (sqrt(5)-\ sqrt(2)\ )(sqrt(5)+sqrt(2))